Module 4: Math

Module 4: Math

Part A: Website Math Videos (www.mathvids.com) and Mathematics Accommodations

The mathematics videos, as shown on the website (http://www.mathvids.com/nctmstandard/show_lessons/1), exemplify numerous strategies and forms of accommodations for mathematics instruction. This website (in its entirety) integrates the reinforcing tools for demonstrating the essential skills of the mathematics curriculum. To explain, the videos reexamine and reiterate the practices, models, strategies, skills, and other principles and/or teachings of mathematics. I would not have these videos be the direct instruction of mathematics, rather an accommodation and/or supplemental activity for students to grasp learning strategies, as active involved students.

The provided website includes a well-informed resource for teachers, as it supplies the description of the video, additional resources, questions answered within each video, staff review, and user review. What makes the videos more useful tools for multiple teachers is the ability to download the video. In doing so, the teacher could incorporate this into the lesson plan, accommodations, or additional activities/extension.

Accommodations the math video, called “How to Subtract Fractions Part 1,” provides are many examples and explicit instruction that is organized with step-by-step presentations (Lerner & Johns, p. 454, 2010). As stated on page 454, students with mild disabilities commonly have “memory deficits that interfere with the automatic learning of computation facts” (Lerner & Johns, 2010). This video reinforces techniques that help children learn and remember (without time restraints) the necessary steps to subtracting fractions.

“Written conversations or dialogue journals are written interactions between teacher and student or between two students” (Lerner & Johns, p. 413, 2010). The math videos interact with the students by communicating the ideas in pictures and numeral form. Using pictures to demonstrate the computational skills, such as multiplying fractions, sets a concrete level for students to grasp the abstract concepts. I find Mr. Burnett’s videos, such as “Multiplying Fractions an Introduction,” as an example for the helping students with disabilities to progress from concrete to abstract thinking and learning. He shows the pictures of the fractions being multiplied (concrete). Then, he explains through comprehensive words and dialogues as the fractions are shown (abstract), and relating the numeral form of fractions with the picture provided in the beginning.

One way I would implement “Subtracting Mixed Numbers with Renaming,” for instance, is after the students have advanced to a level that enables them to work by themselves. In doing so, they can complete the lesson on their own without distracting auditory stimuli (assuming they have earphones). In doing so, this supplies an aid in reinforcing and recalling procedural steps in solving mathematics computations.

Part B: High-Quality Math Instruction: What Teachers Should Know

1. The components of high-quality math instruction include the combination of the following implementations: a standards-based curriculum and evidence-based instructional strategies. A standards-based curriculum includes the content and skills for the math curriculum, as according to NCTM’s Principles and Standards for School Mathematics, includes the knowledge to acquire (content standards) and ways to learn and use knowledge (process standards). The teacher must use the standards, both content and process, according to the grade level curriculum and standards. Evidence-based instructional strategies are the strategies proven in thorough, detailed research to be effective and meaningful for students to grasp mathematical skills and concepts. These strategies are taught with fidelity, or as the researcher, for instance, intended.

2. NCTM content standards encompass the knowledge gained within grades K-12. NCTM process standards enable students with the ways to learn and use the knowledge purposefully from prekindergarten through grade twelve. NCTM process standards entail the appropriate processes students develop for mathematics. NCTM content standards include the following: number and operations, algebra, geometry, measurement, and data analysis and probability. NCTM process standards include the following: problem solving, reasoning and proof, communication, connections, and representation. The content standards are the explicit skills and content for grades K-12. Further, the content standards are comprised of the essential concepts across grade-level curriculums, providing teachers with the focal points they are expected to ensure for student learning. However, process standards are the approaches the students are taught to learn and use, making mathematics curriculum and performance organized, comprehensive, progressive, and conducive to all learners.

3. The evidence-based teaching strategy being implemented begins with explicit teaching, whereby the teacher states the objective and expectation. She also states the importance of taking notes when trying to solve the area of the irregular shape. Another evidence-based teaching strategy is cooperative learning. This video clip demonstrates this strategy which the students collaboratively explain their ideas to solve the mathematical problem. The students are building upon the strategies and skills previously learned in a concrete manner; bridging the abstract concept of area in a conceptual format. This strategy is shown effective and meaningful because all of the students are engaged in the task, as they discuss the problems, and address them with the manipulative (poster board with design). In addition, the teacher questions the thinking process to solve the area, and provides immediate constructive feedback to the group’s explanation and work.

Part C: Dyscalculia Readings Responses


I love the idea of math journals within the mathematics curriculum. This reminds me of my student teaching experience in a sixth grade, where the teacher used math journals for math note-taking, projects, homework assignments, reflections, and timed activities. The students were able to reflect upon their work in a progressive and comprehensive style. They also had a “cheat sheet” in the front that the teacher would explicitly have them add new skills or strategies onto it. This cheat sheet was used as an aid when solving problems. Since my first grade students are learning to write sentences and complete thoughts, I would not find the math journal to be appropriate in this manner. However, I find packets focusing on a certain unit or content standard as an appropriate additional resource for students because I include places for them to write during explicit instruction, and organize the thought process for solving word problems, for example.

Many of my students struggle to use the English language (vocabulary, grammar, verb tense, etc.) correctly for reading and writing. I have also discovered the need for explicit instruction on math vocabulary as an important aspect of the curriculum because the students need to use it as they explain their reasoning and approaches to solving concepts. I recall a wonderful professor at the University of San Diego who taught vocabulary in an explicit manner, providing examples of the new concept. Then, she would have us use the language to solve the problem by communicating our thinking and supporting our use of the terminology in discussions and homework assignments. This article inspires me to establish a cooperative learning time for each math period to further support the math terminology used during oral discussions and in written form.

Marilyn Burns describes the wealth of information provided by what the students understand and how they think in Educational Leadership’s “Looking at How Students Reason” (p. 26). She discusses the importance of intentional and purposeful assessments to offer better alternatives and instructional choices and design. Differentiated instruction must hone in on the students understanding and thinking processes. In doing so, it can support their learning needs to acquire the tools for successfully solving problems. In the beginning of this school year, I assessed my students in mathematics, and found a few students well above the standards and expectations of the curriculum. As I provided additional and extensions for classwork and homework to challenge their critical thinking, I found the gaps between many of their understandings and thinking because they had memorized concepts rather than connect the learning or build upon the skills previously learned. In doing so, I did not provide additional materials to challenge them, rather have them explicitly learn the concepts with the class, then be a coach for students struggling to grasp the numerical concepts. These students gained confidence in using the math terminology and step-by-step procedure acquired.

First-grade science curriculum addresses many opportunities for students to contextualize problem-solving activities by applying the math skills developed and acquired. For instance, using a thermometer during Calendar Time, that allows the students to count in two-unit increments, reinforces skip counting, measurement, and using a thermometer to determine the temperature. When learning about capacities and measurement in mathematics, I teach the properties of matter and how they can change, due to external factors.